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We introduce a class of spin models with long-range interactions---in thesense that they extend significantly beyond nearest neighbors---whose groundstates can be constructed analytically and have a simple matrix product staterepresentation. This enables the detailed study of ground state properties,such as correlation functions and entanglement, in the thermodynamic limit. Thespin models presented here are closely related to lattice gases of stronglyinteracting polar molecules or Rydberg atoms which feature an excluded volumeor blockade interaction. While entanglement is only present between spins thatare separated by no more than a blockade length, we show that non-classicalcorrelations can extend much further and analyze them through quantum discord.We furthermore identify a set of seemingly critical points where the groundstate approaches a crystalline state with a filling fraction that is given bythe inverse of the blockade length. We analyze the scaling properties in thevicinity of this parameter region and show that the correlation lengthpossesses a non-trivial dependence on the blockade length.

Non-classical correlations in a class of spin chains with long-range interactions and exactly solvable ground states